Computational Chemistry

1. Computational Chemistry Tom Grimes 12/13/2001

2. The Basics • Input a molecular structure • In some cases, electronic configuration may need to be known • Three basic types of calculations • Single-point energy • Geometry optimization • Frequency calculation • Interpret the data

3. Single-point Energy • In the simplest terms, it is the energy intrinsic to the structure • Useful for determining the stability of a compound • The structure may be in an excited state • Defines a potential energy surface (PES)

4. Potential Energy Surface

5. PES of HO*

6. Geometry Optimization • Determination of the equilibrium geometry • Generally, the geometry associated with the lowest single-point energy • Can also be used to find transition state geometry by minimizing the energy in all coordinates on the PES except for one • SCF theory finds a stationary point, a place where the energy gradient is zero • May correspond to either a minimum or a saddlepoint

7. Frequency Calculation • Predicts the intensities of the vibrations associated with a molecule • This is useful for predicting the absorption spectra of compounds • It can also be used to verify whether the structure was fully optimized • If it was not fully optimized, reaction coordinates appear as imaginary frequencies. • NMR spectra can also be predicted

8. IR Spectrum of Ethanol Predicted IR Bands Measured IR Spectrum

9. Computational Methods:Molecular Mechanics • Treats molecules classically • Ball-and-spring model • Assumes “ideal” bond angles and lengths • Fastest method • Predicts geometries well • For normal systems, the bond angles and lengths will be close to ideal • Relatively poor prediction of energies • Total energy only takes into account deviation from ideal bond length, bond angles, dihedrals, and van der Waals interactions

10. Computational Methods:Semi-empirical • Based on quantum mechanics, but uses empirical data to simplify the calculations • Fast, but not as fast as molecular mechanics • Produces good energies and good geometries for simple organic compounds

11. Computational Methods:Ab Initio • Calculations based on quantum mechanics, without use of empirical data • Slowest method because it involves approximating a solution to the Schrödinger equation strictly from quantum mechanical principles • Generally finds approximations using self-consistent field (SCF) theory • Produces the best energies and geometries, overall

12. Popular Procedures • Molecular Mechanics • AMBER, DRIEDING, UFF, MMFF • Force-fields, not methods • Semi-Empirical • AM1, PM3, MNDO, CNDO, INDO • Ab Initio • Hartree-Fock, BLYP, DFT methods

13. Basis Sets • A basis set is a set of functions that restrict the electrons considered to specific regions of space • Larger basis sets impose fewer restrictions, and so give better predictions • However, larger basis sets are computationally more expensive

14. Interpretation • Computational data are not a replacement for physical experiments • Keep the basis set and computational method in mind when deciding how much credence to give the result of a calculation • Cross-checking each calculation with another is invaluable • E.g., checking a geometry optimization with a frequency calculation: if imaginary frequencies exist, the structure is not fully optimized and some of the numbers may not be accurate

15. Implementations • Titan • Easy to use GUI • Not as flexible as other programs • Gaussian • No native GUI, but GaussView is available as a front end • Very flexible, but syntax is profuse and often confusing • GAMESS • Text-only interface, even more bare than Gaussian • Free • Well-known and used by researchers

16. DMol3 (Accelrys) • A DFT plugin to the Cerius2 core • Two modules: molecular systems and periodic systems • Advantages • Good implementation of DFT methods • Allows periodic systems, surfaces, solids, as well as gas phase • Parallel • Disadvantages • Requires SGI IRIX (UNIX) workstations

17. A Problem • One of the primary restrictions in carbon nanostructure research is the lack of material • It is expensive and time-consuming to produce bucky-balls/nanotubes • The process of formation is not well understood

18. Nanotube Prices • Very expensive • Run from $300/gram to $1,200/gram • Few sources • Nano-Lab (nano-lab.com) • Carbon Nanotechnologies (cnanotech.com) $360.00 $300.00

19. Research Project • Currently, the most efficient process for nanotube production is the HiPCO process • It is thought that the disproportionation of CO occurs to generate CO2 and carbon, possibly in the form of C2 • Nanotube formation does not occur without the catalyst, but the mechanism of catalysis is unknown • Fe clusters are found at the ends of the tubes, but it is not known whether these are the catalytic agent or whether they form after the tubes

20. Preliminary • Iron pentacarbonyl, Fe(CO)5 • Computational methods are ideal to discover possible mechanisms of catalysis because transition states and energetics can be calculated easily (relative to actually attempting to determine them empirically) and does not require the danger of handling Fe(CO)5

21. Previous Goals • Search existing literature for previous work done on iron carbonyl and dicarbon • Evaluate the computational tools and methods available to us • Find possible iron-dicarbon structures • Compute properties of these compounds

22. Literature Search Results • Provided structural information for Fe(CO)5 that could be verified • Provided the structure of an iron pentacarbonyl dimer and its formation by photolysis • Important because one of the theories of catalysis is nucleation of Fe clusters • HiPCO process expected to provide these conditions • Provided information of the bonding of C2 • Suggested the best methods for computations of iron compounds

23. Formation of the Fe(CO)5 Dimer 2 Fe(CO)5 Fe2(CO)9 + CO Fe3(CO)12

24. Literature Search Results, cont’d • C2 • No sigma orbitals available for bonding • Eta-bonding only • Different from CO ligand bonding CO Bonding C2 Bonding

25. MO Diagrams

26. Literature Search Results, cont’d • Suggested computational methods • DFT – Density Functional Theory • Similar to HF methods, but uses a more general functional for the exchange correlation term in the energy expression • The functional is based on the idea that the minimal energy of a collection of electrons under the influence of an external Coloumbic field is a unique functional of the electron density • CI – Configuration interaction • Is based on approximating the exchange correlation by replacing one or more occupied orbitals with virtual orbitals, basically making a linear superposition of the HF determinant with others

27. Second Goal • The next step was to try to evaluate our tools by reproducing literature values for the structure of Fe(CO)5 • Bond lengths agreed to within ~0.02 Å • Trigonal bipyrimidal geometry was stable • Total energy also agreed with literature

28. Hurdles in Attaining this Goal • Structures containing iron are notoriously difficult to model because the d-orbitals become important in bonding • This significantly increases the time necessary to complete a calculation • Another problem was the difficulty in determining the spin multiplicity of the system • At incorrect multiplicities, the geometry refused to converge upon a stable solution

29. Iron-Dicarbon Compounds • Did not find any in the literature that were helpful • Most in the literature had a bunch of other ligands • It is known that the C2 will be eta-bound to the iron because no sigma orbitals are available • Two stoichiometries were proposed • Fe(C2)4 – tetragonal and square planar • Fe(C2)5 – trigonal bipyrimidal

30. Iron-Dicarbon Structures

31. Another Proposed Structure • This structure was suggested by Smalley and Hauge of Rice University • Optimized using UB3LYP/6-31G • No imaginary frequencies found

32. Properties of Iron-Dicarbon Compounds • Unable to optimize the geometry of any of the stoichiometries • Spin multiplicity unknown • Time-intensive computation limits how fast we can search for viable structures • Not enough time • Since this was at the end of the Summer, there was no time left

33. Conclusion • Search existing literature for previous work done on iron carbonyl and dicarbon • Done • Evaluate the computational tools and methods available to us • Done • Find possible iron-dicarbon structures • Found some, but more work in this area could be useful • Compute properties of these compounds • Begun, but far from done

34. More Research Ideas • Beowulf clusters • Independent distributed • More time needed on the current iron-dicarbon structures • Doing an even more intensive literature search on dicarbon research • Determining possible intermediates • Finding possible pathways for their formation • Finding ways to detect these intermediates • Use the information to make production more efficient

35. References Accelrys, www.accelrys.com Exploring Chemistry with Electronic Structure Methods, 2nd Ed., Foresman and Frisch, Gaussian, Inc. Gaussian 98 User’s Reference, Gaussian, Inc. Titan User’s Guide, Wavefunction, Inc., Schrodinger, Inc. NIST WebBook, webbook.nist.gov/chemistry Previous Work